These wireless or mobile networks are searching for significant gains in terms of capacity, reliability, consumption and the like. Unlike in a landline network, the transmission channel of a wireless network or mobile network is reputed to be difficult and leads to relatively mediocre reliability of transmission. Major progress has been made in recent years in the field of encoding and modulation, especially as regards consumption and capacity. Indeed, in a wireless network where several transmitters/receivers share the same resources (of time, frequency and space), the sending power must be reduced to the utmost.
To make communications reliable, the technique generally used is the ARQ (Automatic Request for Repetition) technique wherein the information is re-transmitted if the receiver detects a presence of errors. This technique calls for error-detection mechanisms and a channel dedicated to signaling. Its main defect is that it increases the transmission time and therefore has little compatibility with real-time applications (telephony for example). Furthermore, new emerging applications such as sensor networks or also the broadcasting of television signals to mobile units are subject towards constraints of complexity and/or consumption that are incompatible with these solutions.
A second and more recent approach relies on relays to improve transmission efficiency. The relay can either “decode and forward” the stream or “amplify and forward” the received signal.
Finally, it has been proposed to combine this technique of relays with the technique known as “network coding”. This approach is described for example by S. Yang and R. Koetter, “Network Coding over a Noisy Relay: a Belief Propagation Approach,” in Proc. IEEE ISIT '07, Nice, France, June 2007.). The relay decodes the two received code words sent respectively by two sources, and then computes and transmits the log-likelihood ratio (LLR) of the bit-by-bit sum modulo 2 of the two code words. Thus, the receiver has three observations available: the two sources and the LLR. This solution has several defects: it is highly sensitive to errors in the relay and above all the analog value of the LLR must be transmitted with sufficient precision (four bits at least) between the relay and the receiver for each bit of the stream sent by the sources, and this is to the detriment of the capacity of the network. A similar approach is proposed by S. Zhang, Y. Zhu, S.-C. Liew, and K. Ben Letaief, “Joint Design of Network Coding and Channel Decoding for Wireless Networks” in Proc. IEEE WCNC '07, pp. 779-784, 11-15 Mar. 2007). However, the authors have studied the reduction of complexity in the relay without touching on the decoding in the receiver.
In these different cases, the decoding is difficult and there is no simple and efficient solution for processing in the receivers.